Cartan geometries on complex manifolds of algebraic dimension zero

Indranil Biswas; Sorin Dumitrescu; Benjamin McKay

doi:10.46298/EPIGA.2019.VOLUME3.4460

Cartan geometries on complex manifolds of algebraic dimension zero

Indranil Biswas
, Sorin Dumitrescu
, Benjamin McKay

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that every compact complex manifold of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type must have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.

Original language	English
Article number	19
Journal	Epijournal de Geometrie Algebrique
Volume	3
DOIs	https://doi.org/10.46298/EPIGA.2019.VOLUME3.4460
Publication status	Published - 5 Dec 2019

Keywords

Algebraic dimension
Almost homogeneous space
Cartan geometry
Killing vector field
Semistability

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10.46298/EPIGA.2019.VOLUME3.4460

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title = "Cartan geometries on complex manifolds of algebraic dimension zero",

abstract = "We prove that every compact complex manifold of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type must have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.",

keywords = "Algebraic dimension, Almost homogeneous space, Cartan geometry, Killing vector field, Semistability",

author = "Indranil Biswas and Sorin Dumitrescu and Benjamin McKay",

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year = "2019",

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AU - Biswas, Indranil

AU - Dumitrescu, Sorin

AU - McKay, Benjamin

N1 - Publisher Copyright: © by the author(s)

PY - 2019/12/5

Y1 - 2019/12/5

N2 - We prove that every compact complex manifold of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type must have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.

AB - We prove that every compact complex manifold of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type must have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.

KW - Algebraic dimension

KW - Almost homogeneous space

KW - Cartan geometry

KW - Killing vector field

KW - Semistability

UR - https://www.scopus.com/pages/publications/85102291831

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DO - 10.46298/EPIGA.2019.VOLUME3.4460

M3 - Article

AN - SCOPUS:85102291831

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VL - 3

JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

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ER -

Cartan geometries on complex manifolds of algebraic dimension zero

Abstract

Keywords

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